The generator is described in the paper: A.-L. Barabási and R. Albert. Emergence of scaling in
random networks. Science, 286:509-512, 1999.

The generator starts with a complete graph of $m_0$ nodes and grows the network by adding $n -
m_0$ additional nodes. The additional nodes are added one by one and each of them is connected to
$m$ previously added nodes, where the probability of connecting to a node is proportional to its
degree.

Note that the Barabàsi-Albert model is designed for undirected networks. Nevertheless, this
generator also works with directed networks where the probabilities are proportional to the sum
of incoming and outgoing degrees. For a more general discussion see the paper: M. E. J. Newman.
The Structure and Function of Complex Networks. SIAM Rev., 45(2):167--256, 2003.